Given that 𝑥 is in the set of
natural numbers, determine the solution set of the inequality negative 𝑥 is
greater than negative 132.
We remember that this symbol
that looks kind of like an N means natural numbers, which are positive
integers. If 𝑥 is in the set of natural
numbers, then it cannot be negative, nor can it be fractional. It must be a positive
integer. If negative 𝑥 is greater than
negative 132, how can we find 𝑥?
If we multiply negative 𝑥 by
negative one, we would get 𝑥. But if we’re going to multiply
or divide with inequalities, we need to remember that when we’re multiplying or
dividing negatives, we must flip the sign. This means we would multiply
both sides of the inequality by negative one. Negative 132 multiplied by
negative one is 132. And then we would flip the
We now have something that says
𝑥 is less than 132. But we also know that 𝑥 is in
the set of natural numbers. So first of all, that means
we’ll need to use set notation, the curly brackets. And secondly, we’re only
interested in the integers less than 132. 𝑥 can’t be negative, and it
can’t be between whole numbers.
The smallest value 𝑥 could be
would be zero. It would then be one, two,
three, continuing. We can use an ellipse to
represent that. And the highest value 𝑥 can be
is 131. We need to be really careful
here. Just because there’s 132 here
doesn’t mean 𝑥 can be equal to 132. 𝑥 must be less than that. And so the largest integer that
is less than 132 is 131. Under these conditions, 𝑥 can
be all the positive integers between zero and 131.